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# help

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Let

$$f(x) = \left\{ \begin{array}{cl} ax+3 & \text{ if }x>0, \\ ab & \text{ if }x=0, \\ bx+c & \text{ if }x<0. \end{array} \right.$$

If f(2)=5, f(0)=5, and f(-2)=-10, and a, b, and c, are nonnegative integers, then what is a+b+c?

Jan 5, 2020

#1
+22080
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2 is in the first category of x>0

so   f(2) = ax+3           a(2) + 3 = 5     then      a = 1

0 is in the second category of x = 0

then f(0)  would be    ab = 5       a, we found is 1    then   b  = 5

-2 is in the third category x<0

then f(-2) = bx+c  =-10                   b we found to be 5

5(-2) +c = -10           so c =0

a+b+c=1+5+0=6

Jan 5, 2020
#2
+245
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ok thank you! i finally understand these problems now..

atlas9  Jan 8, 2020